The index of refraction of an object in the visible wavelength domain range can be measured by interferometers, where the index of refraction in the X-ray domain can be measured by X-ray interferometry. In most of the interferometric measurement modalities, the fringe is formed by a coherent light source (for example laser) and optical components such as mirrors and lenses. Coherent light is split into two or more light beams, in either amplitude or space, by optical components such as a beam splitter and mirrors. One of the split beams (Object beam) passes through an object to be tested. The object induces an additional optical path length along the object beam. The modulation of the optical path is detected as a distortion of the fringe pattern by superposition of the other beam, (a reference beam) on top of the modulated object beam. The interferometric measurement is applicable for X-rays, however there are specific challenges for interferometric measurement in the X-ray domain. Coherent X-ray sources, such as synchrotron radiation light sources and X-ray lasers, are not as practical as coherent light sources in the visible domain. Also, the variation of X-ray optics is limited. For example, an X-ray lens has extremely small lens power due to the small differences in the index of refraction between air and the material. This lack of a handy coherent X-ray light source and the optical components for interferometry is overcome by Talbot interferometry by using an incoherent and a low brilliance X-ray source. FIG. 1 shows a schematic diagram of a prior art Talbot interferometry. In front of a conventional incoherent X-ray source such as electron-bombarded tungsten, an absorption grating (Silicon grating filled with Gold” Au/Si grating) is placed. Silicon is highly transparent to X-ray whereas Au is an absorptive material. The Si grating is filled with Au. The filled Au part blocks the X-rays, as a result, the Au/Si grating (G0 grating) creates an array of line sources, which are partially coherent themselves but are mutually incoherent with each other. As each partially coherent line source emits a cylindrical wave, the cylindrical wave is diffracted by a second phase grating made of Silicon (G1 grating). Generally, such a phase grating diffracts the incoming wave into multiple higher diffraction orders. As a special example, if the phase depth of the G0 grating is tuned to Pi by adjusting the height of the grating wall to the specific X-ray wavelength, the phase profile is a rectangular one, only a plus and minus 1st order diffraction wave exists. The diffracted cylindrical waves propagate and interfere with each other. As a result, a fractional Talbot fringe image is formed behind the G1 grating. In the absence of an object, the fringe forms straight lines and the line lies along the G0 and G1 grating. With the presence of an object (either in front of or behind the G1 grating), the straight fringe line is distorted due to the modulation of the phase along X-ray optical path. The distortion of the X-ray fringe is a spatial derivative of the phase profile induced by the object, and is detected by an X-ray detector array. The X-ray detector array includes a scintillator, which converts the X-ray photons to light photons, and a fiber optics plate, and photo diode array. To detect the X-ray fringe, another absorption grating (G2 grating) is placed in front of the detector. Because the pitch of the fringe is generally much smaller than that of the photo detector array, the pitch of the G2 grating is matched to that of the X-ray fringe. To detect the spatial distortion of the fringe line, the G2 grating is mechanically scanned in a direction perpendicular to the fringe lines. At each scanning step, a signal is detected. Typically, the scanning step of the G2 grating is ¼ or less of the pitch of the X-ray fringe. The detector signal is recorded as a function of the scanning step. Such a fringe scanning method, which is commonly used to detect phase from fringe pattern, is applied to detect the amount of the fringe distortion at each of the pixels. Finally, the induced phase by the object is computed by integrating the measured fringe distortion, using the relationship between the fringe shift and the spatial differential of the phase profile. Since the X-ray is not deflected severely by the object, the spatial phase distribution of the object is calculated by back tracing the x-ray from the detector to the source. This procedure reconstructs the spatial phase profile. A standard CT reconstruction algorithm can be also applied to reconstruct 3-D phase profile of the object.
The Talbot interferometer is an excellent way to enable X-ray interferometry without using a costly coherent X-ray source, by just using the three gratings. However there are fundamental drawbacks due to the usage of gratings: narrow field of view (FOV), a long data acquisition time due to mechanical motion of G2 grating, and the costly and difficult fabrication of large gratings. This is especially true for applications for a wide FOV, and for high throughput application such as screening of a luggage at airport, where the small FOV and long scanning time is a serious problem.
Turning now to the scanning time, typically, the X-ray fringe is detected by mechanically scanning an analyzer grating (G2 grating). The G2 grating is a high aspect ratio grating made of Au, and is placed in front of a scintillator-based X-ray detector array. Such a mechanical scanning requires a high-precision control of motion of the grating (on the order of tens of nanometers), because at least four, ideally 16 steps of scanning is needed for typical X-ray fringe pitch of 5-10 μm. As a result the data acquisition rate is primarily limited by the mechanical scanning time.
Furthermore, the mechanical scanning becomes significantly more difficult, where the size of the grating increases as the size and weight of the Au/Si grating increases. For high X-ray photon energy applications, such as screening luggage at an airport, the fabrication of the Au/Si grating becomes a serious problem. Fabricating of the Au-grating having an area equivalent to the size of a piece of luggage (typically on the order of meter) is very difficult, where the fabrication process of the grating is basically a semiconductor process by using a Si substrate and employing lithography followed by anisotropic KOH etching, metallization, side wall passivation, and electroplating of Au. Fabrication of such a large grating is not easy because the need for a large area lithography machine, etching chamber and electro plating chamber, while controlling the process conditions for such a large area substrate. In addition to the size of the grating, the aspect ratio, meaning the ratio of the height of grating wall to the extent of opening region, becomes large (1 to 50 for 100 KeV X-ray photon energy), which imposes serious challenges for the grating fabrication. Ideally the wall height is on the order of couple of hundred micrometers (˜500 um) for a high energy X-ray application, whereas the width of the opening is on the order of tens of micrometers. Thus the aspect ratio of the grating is 10 or larger. The fabrication of such a high aspect ratio grating having a square meter area is a serious challenge. In addition, the grating is technically a thin gold plate having an extent of a square meter and thickness of 250 μm, thus making the handling of such a Au plate a problem too.
For the FOV of a high aspect ratio grating is relatively very small (on the order of degrees), the high aspect ratio G2 grating effectively detects the fringe if the X-ray propagates close to parallel to the grating side-wall, otherwise the G2 grating does not provide sufficient contrast of the signal while stepping it. The FOV of the G2 grating is approximated by ArcTan(1/AspectRatio)˜1/AspectRatio. For an aspect ratio of 10, the FOV is only ±2.8 degrees, which is too small to inspect large object while limiting the overall length (eg. the source to detector distance) as small as 1-2 meters.
In summary, mechanical scanning of the Au/Si grating has several drawbacks, such as slow detection due to mechanical scanning, small FOV and costly and long lead time fabrication of high aspect ratio Au gratings.
What is needed is a detector system that eliminates the analyzer grating from the system, and enables for motionless fringe detection having a large FOV.